Abstract
A simple parametrization for most perfect magic (MPM) squares is derived. This parametrization permits to calculate their powers and eigenvalues as well as their Moore–Penrose, group, and core inverses in an easy fashion. Such properties as EP-ness, normality, symmetry, and partial isometriness of the MPM squares are also characterized. Moreover, their eigenspaces are identified along with some properties of such squares with prime entries.
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